FORMA EN QUE SE DEVENGA Y ANTICIPOS

In this section we will first discuss graphene and TMDC samples and the effect of electro- static disorder as one of the major extrinsic sources of scattering and decrease of mobility for layered materials. Furthermore, we will introduce EDLT as a device where disorder can be manipulated, which allows us to explore device behavior in different regimes.

5.2.1 Disorder in graphene devices

Graphene was the first material in the family of two-dimensional materials to attract se- rious research efforts [1, 2, 3]. From the first sight, graphene and other two-dimensional materials look very similar to conventional two-dimensional electron gas (2DEG), which could be found for instance in high-mobility electron transistor (HEMT) structures [123]. We stress several important differences. First, 2DEG is completely buried between the semiconducting layers which form it, making it a clean electronic system, screened from

any types of external disorder. 2D materials, fabricated on standard SiO2substrates are

immediately exposed to potential variations and roughness of the substrate [124]. Sec- ond, depending on the sample design, the semiconducting channel can be exposed to atmospheric adsorbates (for example in back gate geometry) and atmospheric species can act as scattering centers. Third factor, degrading sample quality, which is important for almost all devices in the field, are the processing residues, for instance polymer resist residues, which appear to be very difficult to remove [125]. We point to the fact, that all abovementioned effects appear to be more detrimental in the case of monolayers, where charge carriers in fact reside very close to the surface of the material and where screening from disorder is barely possible.

The historical development of the graphene research field, starting from the first samples, where quantum hall effect (QHE) was observed [126, 127] to recent detailed transport studies on various types of "clean" samples [14, 15] showed gradual improvement of

sample quality. Placing graphene on low density h-BN instead of SiO2substrates already

improved the quality of investigated samples [128, 129]. The importance of extrinsic sources of disorder was fully revealed, when first residue-free encapsulation of graphene in two-dimensional defect-free dielectric h-BN was demonstrated [14]. Certain techniques of transfer have been developed, which allowed to fully avoid contact between graphene and any polymer and to protect it from atmospheric adsorbates [14, 130]. The example of graphene, encapsulated in conventional way in h-BN [131], is shown on Figure 5.2.1a, where formed hydrocarbon bubbles are shown. Figure 5.2.1b shows high-resolution ADF- STEM micrograph of "clean" graphene sample [14], with no visible residues and perfect interfaces. Figure 5.2.1c, d show the basic transport characterization [14]. In contrast

5.2. Electrostatic disorder

a

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Figure 5.1 – Comparison between graphene samples, produced with different transfer methods. (a) Bright-field TEM micrograph of h-BN/Graphene/h-BN sample, with typical hydrocarbon bubbles, formed at the interface. Scale bar - 25 nm. Adapted by permis- sion from Macmillan Publishers Ltd: [Nature Materials] S.J. Haigh, A. Gholinia, R. Jalil, S. Romani, L. Britnell, D.C. Elias, K.S. Novoselov, L. A. Ponomarenko, A.K. Geim, and R. Gorbachev, "Cross-sectional imaging of individual layers and buried interfaces of graphene- based heterostructures and superlattices", Nature Materials, vol. 11, no. 9, pp. 764-767, © (2012). (b) High-resolution cross-section ADF-STEM image of h-BN/G/h-BN device, produced with residue-free transfer method. (c) Electrical characterization of the "clean" h-BN/G/h-BN stack. Left inset - optical micrograph of the sample under investigation in van der Pauw geometry. Right inset - zoom in to R-Vgatecharacteristic at 300K and at 1.7K.

Curve at 1.7K shows negative resistance on hole side, indicating ballistic transport on the

scale of approximately 15μm. (d) Comparison of room temperature mobility in graphene

and other two-dimensional systems as a function of carrier density. (b)-(d) Adapted with permission from L. Wang, I. Meric, P.Y. Huang, Q. Gao, Y. Gao, H. Tran, T. Taniguchi, K. Watanabe, L.M. Campos, D.A. Muller, J. Guo, P. Kim, J. Hone, K.L. Shepard, C.R. Dean, "One-Dimensional Electrical Contact to a Two-Dimensional Material", Science, vol. 342, no. 6158, pp. 614-617, © (2013) The American Association for the Advancement of Science.

to conventional samples on SiO2and even not optimized samples on h-BN, the "clean"

5.2.2 Disorder in TMDCs

This approach could be universally employed for other two-dimensional materials, in particular to semiconducting TMDCs. TMDCs differ from graphene in many aspects, including the ranges of mobilities and defect types, but the possibility to remove most of the extrinsic sources of disorder allows us to significantly improve the sample quality [16]. We can quantify the sample quality based on the values of low temperature mobility.

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Figure 5.2 – Electrical transport properties of semiconducting TMDCs encapsulated in

h-BN. (a) Mobility in h-BN encapsulated MoS2samples as a function of temperature and

thickness. Adapted by permission from Macmillan Publishers Ltd: [Nature Nanotechnol- ogy] X. Cui, G.-H. Lee, Y. D. Kim, G. Arefe, P.Y. Huang, C.-H. Lee, D.A. Chenet, X. Zhang, L. Wang, F. Ye, F. Pizzocchero, B. S. Jessen, K. Watanabe, T. Taniguchi, D.A. Muller, T. Low, P. Kim, and J. Hone, "Multi-terminal transport measurements of MoS2using a van der Waals

heterostructure device platform", Nature Nanotechnology, vol. 10, no. 6, pp. 534-540, ©

(2015). (b) Mobility in h-BN encapsulated multilayer WS2samples as a function of temper-

ature. © (2016), Z. Wu, S. Xu, H. Lu, A. Khamoshi, G.-B. Liu, T. Han, Y. Wu, J. Lin, G. Long, Y. He, Y. Cai, Y. Yao, F. Zhang, and N. Wang, "Even–odd layer-dependent magnetotransport of high-mobility Q-valley electrons in transition metal disulfides", Nature Communications, vol. 7, p. 12955, 2016.

The point we would like to emphasize is that so far even in the cleanest samples low temperature transport in monolayers seems to be more sensitive to intrinsic or extrinsic

values of disorder. For example, work [16] focuses on encapsulation in h-BN of MoS2

samples of different thickness, as shown on Figure 5.2.2a. It appears, that monolayers

have lowest mobility. Transport in h-BN encapsulated monolayer WSe2has been shown

to have similar quality with low temperature mobility in the order of 2000 cm2· V−1· s−1, while multilayers exhibit higher low temperature carrier mobility [132] on the order of 4000 cm2· V−1· s−1.

We stress that h-BN encapsulation, although being a widespread approach for improve- ment of transport properties, is not the only one available. The strong side of h-BN use is

5.2. Electrostatic disorder

the possibility to pick up other 2D materials with this dielectric and avoid any contact with polymer and process flow residues [14]. However, any substrate without dangling bonds, for instance parylene [133], could lead to significant improvement of transport properties and less scattering.

In this Section we showed the importance of different types of extrinsic sources of disorder. We put optimization of material itself and intrinsic scatterers aside for now [101]. It is clear that understanding of disorder and its influence on transport properties is essential for optimization of high-performance devices based on TMDCs and other 2D materials for future applications.

5.2.3 EDLT as a disorder modulating tool

Discussion in the previous sections focused on the samples of different quality and compar- ison between them. We emphasize, that in each particular approach to sample fabrication technique disorder will be different but will have a fixed value. EDLT samples are known to have lower carrier mobility than "clean" ones. This is the initial sign of electrostatic disorder effect, originating from ionic liquids or polymer electrolytes. This can be seen on

examples of such systems as monolayer WSe2, where low temperature mobility in EDLT

[58] is an order of magnitude lower than in encapsulated samples [103]. Similar tendency is observed for example in black phosphorous samples [134], [135], [136],[137].

The origin of disorder could be qualitatively understood from Figure 5.3, where the cross section of interface between the semiconductor and the ionic media is schematically illustrated. Here, ions of different signs are located at different distances from the semicon- ducting channel and the in-plane distance between the ions varies as well. This random pattern can be understood if we consider the situation where two types of ions, which can be approximated as spheres, having imbalance in the amount of positive and negative ones, have to be tightly packed on the surface of our material. This rough electrostatic potential appears to be in the close vicinity of the semiconducting channel (typically 10-20 Å) and acts as extrinsic disorder for the carriers, travelling inside the semiconducting channel.

The only limitation for disorder modulation appears to be the fact that disorder strength is changed together with carrier density. Additional solid back gate leads to more flexible situation, where these two quantities could be modulated in an independent manner, changing electrolyte voltage at high temperatures and back gate voltage after freezing of electrolyte, thus exploring different carrier densities at the fixed value of disorder strength. We also notice that monolayers might be more sensitive to the abovementioned effect of disorder. The reason for that is the screening of the electric field in the bulk [49]. As

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Current flow direction

Semiconductor

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Polymer electrolyte

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Figure 5.3 – Schematic cross section of interface between electrolyte and semiconducting channel in EDLT.

accumulation is happening in the top 2-3 layers (screening for WSe2is in the order of 2-3

nm). In case there is residual doping in the bulk, it will still provide conductivity (Figure 5.4a, sample is still conducting at the region around Vg= -2V), while the electrons in the

deep layers will be screened from disorder by the upper ones.

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Figure 5.4 – EDLT based on bulk WSe2. (a) Sheet conductivity as a function of gate voltage.

(b) Schematic cross section of the interface between ionic liquid and WSe2. Adapted by

permission from Macmillan Publishers Ltd: [Nature Physics] H. Yuan, M.S. Bahramy, K. Morimoto, S. Wu, K. Nomura, B.-J. Yang, H. Shimotani, R. Suzuki, M. Toh, C. Kloc, X. Xu, R. Arita, N. Nagaosa, and Y. Iwasa, "Zeeman-type spin splitting controlled by an electric field", Nature Physics, vol. 9, no. 9, pp. 563-569, © (2013).

Experimentally, the effect of disorder has been observed in the number of works. In the Sections 5.2.1 and 5.2.2 we mentioned, that h-BN encapsulated samples in general have higher mobility due to clean interface, low roughness and good charge homogeneity of the substrates than for instance EDLT based on similar materials. However, we notice, that there are differences in sample fabrication procedures and thus the comparison between